Every l.s.c\. mapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) $G_\delta $-subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.
@article{118693,
author = {Valentin G. Gutev},
title = {Continuous selections, $G\_\delta $-subsets of Banach spaces and usco mappings},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {35},
year = {1994},
pages = {533-538},
zbl = {0840.54023},
mrnumber = {1307280},
language = {en},
url = {http://dml.mathdoc.fr/item/118693}
}
Gutev, Valentin G. Continuous selections, $G_\delta $-subsets of Banach spaces and usco mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 533-538. http://gdmltest.u-ga.fr/item/118693/
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